Japanese prosecutors are to question a former president of disgraced Olympus Corp over an accounting scandal at the camera and medical device maker, as investigators probe for possible involvement of organised crime, media reports said on Friday.

Tsuyoshi Kikukawa, who quit as company president on October 26, and two others face voluntary questioning as early as this weekend, Kyodo news agency reported.

Olympus, a world leader in diagnostic endoscopes, has admitted hiding losses for decades through improper accounting, but has yet to say how far this concealment went and what writedowns it will now need to take.

The company's new president, Shuichi Takayama, has blamed Kikukawa, Vice-President Hisashi Mori and internal auditor Hideo Yamada for the cover-up, and said he would consider criminal complaints against them. Mori has been fired and Yamada has offered to resign.

The New York Times reported that Japanese officials are investigating an apparent $4.9 billion (3.1 billion pounds) hole in the accounts of Olympus as well as possible involvement of organised crime.

Olympus made payouts amounting to many times the losses it sought to hide, and investigators suspect much of the additional money went to crime groups, the newspaper said, citing a memo prepared by investigators.

That memo says authorities want to find out if Olympus worked with crime syndicates to obscure the losses, and paid them huge sums of money for their help, the paper said, noting the memo was circulated at a recent meeting of officials from Japan's Securities and Exchange Surveillance Commission (SESC), the Tokyo Prosecutors Office and Tokyo Metropolitan Police.

A Tokyo police spokeswoman confirmed that a probe of Olympus was under way, but declined to give details. The Tokyo Prosecutors Office and SESC declined comment.

Olympus declined comment on the media reports.

Links between companies, yakuza gangsters and politicians have a long tradition in Japan, and authorities have been trying to crack down for decades, most recently with laws targeting not only crime syndicates but firms that do business with them.

The New York Times quoted the memo as saying Olympus had paid a total of 481 billion yen (3.96 billion pounds) through questionable acquisition payments, investments and advisory fees stretching between 2000 and 2009, but only 105 billion yen (862.72 million pounds) had been booked in its financial statements.

FUNDS HARD TO TRACE

So far, Olympus has admitted to improperly accounting for only part of $1.3 billion in payments linked to mergers and acquisitions going back to 2006 , though an independent panel commissioned by the firm to investigate the matter was still trying to get to the bottom of the issue.

A large share of these payments went to obscure Cayman Islands firms, making it difficult to trace the money.

Olympus said on Thursday that Mori had told the company none of the funds involved in the cover-up scheme had gone to anti-social forces -- a Japanese euphemism for gangsters -- but the firm was waiting for the independent panel's report, which is due early next month.

Olympus has lost more than 70 percent of its market value since the scandal broke last month, with major shareholders Nippon Life and Mitsubishi UFJ Financial Group (MUFG) sharply reducing their shareholdings in the company.

Four MUFG units cut their collective Olympus stake to 7.61 percent from 10 percent, a regulatory filing showed on Friday.

Olympus shares were down around 14 percent in afternoon trade, threatening to snuff out a rally this week on investor hopes that the company would avoid being delisted.

Delisting would effectively cut Olympus off from equity capital markets, constraining its funding and making it harder for its lenders to keep supporting the firm in its battle to avoid having to sell off its core businesses.

The Asian Corporate Governance Association, an advocacy group whose members include institutional investors managing more than $10 trillion worth of assets, urged the stock exchange on Friday not to delist Olympus -- a move that could damage Japan's reputation among global investors.

We believe shareholders have already suffered enough due to the actions of Olympus executives ... and a delisting would also harm Japan's reputation among international investors, the group wrote in a letter dated November 17.

Proof that organised crime was involved could force the Tokyo exchange to delist Olympus shares, and could make it hard, if not impossible, for banks to make fresh loans to the firm.

If a company is found to have problems, like the involvement of anti-social forces, banks are not able to give support, Katsunori Nagayasu, chairman of the Japanese Bankers Association and MUFG president, said on Thursday.

Lawyer Shin Ushijima, a former prosecutor, said organised crime involvement at first blush appeared unlikely, but could not be ruled out, if gangsters had gotten wind of the loss cover-ups and sought payments to stay silent.

I don't think it's likely, but we cannot deny it (the possibility), he said. If the yakuza got some information, it means that someone spoke about it and that is very unlikely.

Other experts say gangsters often begin by blackmailing an executive or company over one scandal, and then push for more money to keep that original payoff a secret.

(Writing by Linda Sieg; Editing by Mark Bendeich and Ian Geoghegan)